SOLUTION: Please help, I'm gettin no where with it. Car thieves steal on automobile out of 400 of a certain type every year in a certain city. What annual net premium should an owner pay for

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Question 175401: Please help, I'm gettin no where with it. Car thieves steal on automobile out of 400 of a certain type every year in a certain city. What annual net premium should an owner pay for theft insurance in the amount of $16,000 on the certain type of car?
Answer by stanbon(75887) (Show Source):
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Car thieves steal on automobile out of 400 of a certain type every year in a certain city. What annual net premium should an owner pay for theft insurance in the amount of $16,000 on the certain type of car?
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That is an "expected value" problem.
The random variable is "cost to the car owner".
Cost is -x if his car is not stolen or (16000-x) if it is stolen
The probability of -x is (399/400); the prob of (16000-x) is (1/400)
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The expected value is (399/400)(-x) + (1/400)(16000-x)
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For the owner to "break even" this expected value should be zero.
(399/400)(-x) + (1/400)(16000-x) = 0
-399x + 16000-x = 0
-400x = -16000
x = $40.00 (His annual cost should be $40).
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Cheers,
Stan H.